"We're going to build a wall," Trump told reporters here at his first news conference in six months and denied that it would be a "fence".
"I could wait about a year-and-a-half until we finish our negotiations with Mexico, which will start immediately after we get to office, but I don't want to wait. (Vice President- elect) Mike Pence is leading an effort to get final approvals through various agencies and through Congress for the wall to begin," Trump explained.
But Mexico has said it would never pay for the wall.
"I don't feel like waiting a year or a year-and-a-half. We're going to start building. Mexico in some form, and there are many different forms, will reimburse us and they will reimburse us for the cost of the wall," Trump said.
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"That will happen, whether it's a tax or whether it's a payment -- probably less likely that it's a payment. But it will happen. So, remember this," he said.
"What's the difference?" Trump asked.
"I want to get the wall started. I don't want to wait a year-and-a-half until I make my deal with Mexico. We probably will have a deal sooner than that," he said as he praised the Mexican government.
"Mexico has been so nice, so nice. I respect the government of Mexico. I respect the people of Mexico. I love the people of Mexico. I have many people from Mexico working for me. They're phenomenal people. The government of Mexico is terrific. I don't blame them for what's happened. I don't blame them for taking advantage of the United States," he said adding he wished American politicians were as smart.
Mexican migrants from the United States if he elected.
Meanwhile, Mexico's new foreign minister today said that there is "no way" that his country will pay for the wall.
Luis Videgaray, who was appointed by President Enrique Pena Nieto last week to seek "constructive" relations with the Trump administration, told the Televisa network that Mexico "will not cede" on issues related to "national sovereignty."
"The United States has the right to protect its borders. What is inadmissible, and which would deeply violate the dignity of all Mexicans, is to expect Mexico to pay for infrastructure of the United States," Videgaray told Radio Formula.
Trump had called Mexican migrants "rapists" and drug dealers during the presidential campaign and vowed to make their country pay for a massive wall across the border.
The Republican real estate billionaire, who assumes office on January 20, has threatened to fund the giant wall by tapping into the billions of dollars in remittances that Mexican migrants in the US send back home.